Compressibility effect in compressible turbulent channel flows

In this study, direct numerical simulations are carried out in compressible turbulent channel flows at Mach numbers 3 and 4.3. Combining the previous numerical cases with Mach numbers 0.3, 0.5 and 1.5, a compressible turbulent channel flow database covering the Mach number range from 0.3 to 4.3 at bulk Reynolds number approximately 6000 is obtained. Using this database, we studied the statistical behavior of the flow fields, the velocity and temperature streak structures, and the balance equation of temperature variance. The results show that the statistics related to the velocity field, the temperature field, and the velocity-temperature coupling quantities show better collapse behaviors in the semi-local coordinates, which demonstrates that the turbulent statistics depend mainly on the mean density and viscosity, indicating that the Morkovin hypothesis is applicable in the current Mach number range (0.3-4.3). Furthermore, the findings demonstrate that at high Mach numbers, compressibility is significantly enhanced, which makes the near-wall streak structures more stable. However, the proportion of the dilatation dissipation (due to the compressibility) in the total turbulent dissipation is still small and can be ignored.